A parsimonious approach to predict regions affected by sewer-borne contaminants in urban aquifers

Leaky urban drainage networks (UDNs) exfiltrating wastewater can contaminate aquifers. Detailed knowledge on spatiotemporal distributions of water-dissolved, sewer-borne contaminants in groundwater is essential to protect urban aquifers and to optimize monitoring systems. We evaluated the effect of UDN layouts on the spreading of sewer-borne contaminants in groundwater using a parsimonious approach. Due to the UDN’s long-term leakage behavior and the existence of non-degradable sewer-borne contaminants (equivalent to a conservative and constant contaminant source), we employed a concept of horizontal line sources to mimic the UDN layout. This does not require the consideration of bio-degradation processes or temporal delay and effectively bypasses the vadose zone, thus reducing computational requirements associated with a full simulation of leakages. We used a set of synthetic leakage scenarios which were generated using fractals and are based on a real-world UDN layout. We investigated the effects of typical leakage rates, varying groundwater flow directions, and UDN’s layouts on the shape of the contaminant plume, disregarding the resulted concentration. Leakage rates showed minimal effects on the total covered plume area, whereas 89% of the variance of the plume’s geometry is explained by both the UDN’s layout (e.g., length and level of complexity) and groundwater flow direction. We demonstrated the potential of applying this approach to identify possible locations of groundwater observation wells using a real UDN layout. This straightforward and parsimonious method can serve as an initial step to strategically identify optimal monitoring systems locations within urban aquifers, and to improve sewer asset management at city scale. Supplementary Information The online version contains supplementary material available at 10.1007/s10661-023-12027-6.

Table S2.HLSC characteristics of artificial sewer network.Levels of complexity -LC 2 and 3.
Depending on the position of the connection of secondary pipe (PS) to the main pipe and the number of tertiary pipes, the covered drainage area (  ) and location of the centroid may change

Figure
Figure supplements [Figure S1 to S4]

Fig. S4
Fig. S4 Edges and covered areas of contamination plume generated by whole subnetwork (type

Table supplements [Table S1 to S10]Table S1 .
Characteristics of the HLSC representing one single pipe.Level of complexity -LC 1.All HLSC of length 1000m have the same geometric centroid and different angle formed by the HLSC and the flow vectors or width.When the width of the HLSC changes, the HLSC represents a new area of leakage

Table S3 .
Characteristics of HLSC derived from real-world UDN (subnetworks 1 to 6 and whole networktype 7) and comparison among generated contaminant plumes.L: Length of the HLSC;   : Area covered by HLSC; M: total injected mass after 10 years of simulation; percentage of injected mass (%);  , : area of the contaminant plume; percentage (%) of the area of the plume generated by individual HLSC (type 1 to 6) compared to plume generated by the whole network (type 7); location of centroid of plume (x and y coordinates)

Table S4 .
Characterization of contaminant plumes generated by a single HLSC, level of complexity LC 1, forming four different intersection angles α with the groundwater velocity vectors.The individual plume characteristics are  , : area of the contaminant plume, location of centroid of plume (x and y coordinates), width and length of the plume (wp and Lp respectively);   represents the relative areas of contaminant plumes

Table S5 .
Characterization of the contaminant plume generated by one HLSC having different widths and two different intersection angles α with the groundwater velocity vectors.The individual plume characteristics are  , : area of the contaminant plume, location of centroid of plume (x and y coordinates), width and length of the plume (wp and Lp respectively);   : represents the relative areas of contaminant plumes

Table S6 .
Characteristics of HLSC and generated contaminant plumes shown in Figure4.LC: by the HLSC representing the UDN;  1: groundwater direction along x-axis;  2: groundwater direction along y-axis; LR1: constant leakage rate;  , : total area of the contaminant plume; xp: coordinate x for the centroid of the contaminant plume; yp: coordinate y for the centroid of the contaminant plume;   : relative area of the contaminant plume for a given HLSC in relation to the base case scenario

Table S7 .
ANOVA used to identify the factors with a significant influence on the spreading of   .The ANOVA shows a test of statistical significance that compares the mean square versus the estimated experimental error.In this case all factors have a p-value less than 0.05 (see column Pr(>F)),showing that their means are significantly different than zero with a 95% of confidence level.
pipe (PS); and area covered by the HLSC (  ).The variable response was   .Adjusted R-squared: 0.8903, shows that the model explains 89% of the variability

Table S8 .
Pearson correlation matrix among HLSC and contaminant plume characteristics.  : relative area of the contaminant plume.Length of the HLSC is positive correlated to the number of pipes, area covered by the HLSC and the LC: Level of complexity of fractal UDN (1, 2 or 3).L: total length of HLSC; Npipes: number of connected pipes; AHLSC: area covered by the HLSC representing the UDN; α: angle of connection of secondary pipe to main pipe;

Table S9 .
Testing the statistically significant differences between the means of the relative area of the plume (  ) obtained by the scenarios, in which the groundwater direction () and leakage rate () were varied using a t-test. 1: groundwater direction along x-axis;

Table S10 .
Comparing two HLSC having same geometry, groundwater flow direction (GWD) but different leakage rate (LR).BC shows the base case scenario.LC: Level of complexity of fractal UDN (1 or 2); Intersection angle (α): angle of connection to main pipe; PS: position of connection of secondary pipe to main pipe, PS 12: secondary pipes connected to positions 1 and 2; L: total length of HLSC; Npipes: number of connected pipes; xHLSC: coordinate x for the centroid of the HLSC representing the sewer network; yHLSC: coordinate y for the centroid of the HLSC representing the sewer network; AHLSC: area covered by the HLSC representing the UDN;  1: groundwater direction along x-axis; LR1: constant leakage rate; LR2: variable leakage rate;  , : total area of the contaminant plume; xp: coordinate x for the centroid of the contaminant plume; yp: coordinate y for the centroid of the contaminant plume;   : relative area of the contaminant plume